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AnnyKZ [126]
2 years ago
10

Convert 2FA.C8 base 16. express in Octal form, Quinary or pental form and Binary form​

Mathematics
1 answer:
Sunny_sXe [5.5K]2 years ago
4 0

Using base conversion method, 2FA.C8 base 16 can be expressed as:

  • 1372.628 in octal
  • 11022.3423120034 in pental
  • 1011111010.11001 in binary

<h3>What is 2FA.C8 base 16 expressed in Octal form?</h3>

To express 2FA.C8 in octal form, it is first converted to a decimal form as follows:

where:

F = 15

A = 10

C = 12

2FA.C8 = 2 × 16^2 + F × 16^1 + A × 16^0 + C × 16^-1 + 8 × 16^-2

2FA.C8 = 762.7812510 in decimal.

Then, convert 762.7812510 to octal as follows:

  • First the integral part is converted to octal by repeated division by 8.
  • The fractional part is converted to octal by repeated multiplication by 8 until we get to zero (here, we calculate up to ten digits)
  • add the integral and fractional part together

762 / 8 = 95 remainder 2

95 / 8 = 11 remainder 7

11 / 8 = 1 remainder 3

1 / 8 = 0 remainder 1

762 = 1372

Then;

0.78125 × 8 = 6 + 0.25

0.25 × 8 = 2 + 0

0.78125 = 0.62

Therefore, 762.78125 in decimal = 1372.628 in octal

<h3>What is 2FA.C8 base 16 expressed in pental form?</h3>

To convert 2FA.C8 base 16 to pental form, we use its value in decimal for conversion.

  • 2FA.C8 base 16 = 762.7812510 base 10

Then, convert 762.7812510 to pental as follows:

  • First the integral part is converted to pental by repeated division by 5
  • The fractional part is converted to pental by repeated multiplication by 5 until we get to zero (here, we calculate up to ten digits)
  • add the integral and fractional part together

762 / 5 = 152 remainder 2

152 / 5 = 30 remainder 2

30 / 5 = 6 remainder 0

6 / 5 = 1 remainder 1

1 / 5 = 0 remainder 1

  • 762 in decimal = 11022 in pental

Then 0.78125 to pental:

0.78125 × 5 = 3 + 0.90625

0.90625 × 5 = 4 + 0.53125

0.53125 × 5 = 2 + 0.65625

0.65625 × 5 = 3 + 0.28125

0.28125 × 5 = 1 + 0.40625

0.40625 × 5 = 2 + 0.03125

0.03125 × 5 = 0 + 0.15625

0.15625 × 5 = 0 + 0.78125

0.78125 × 5 = 3 + 0.90625

0.90625 × 5 = 4 + 0.53125

Thus, 0.78125 in decimal = 0.3423120034 in pental

Therefore, 762.78125 in decimal = 11022.3423120034 in pental.

<h3>What is 2FA.C8 base 16 expressed in Binary form?</h3>

To convert 2FA.C8 base 16 to binary form, we use its value in decimal for conversion.

  • 2FA.C8 base 16 = 762.7812510 base 10

Then, convert 762.7812510 to binary as follows:

  • First the integral part is converted to binary by repeated division by 2
  • The fractional part is converted to binary by repeated multiplication by 2 until we get to zero (here, we calculate up to ten digits)
  • add the integral and fractional part together

762 / 2 = 381 remainder 0

381 / 2 = 190 remainder 1

190 / 2 = 95 remainder 0

95 / 2 = 47 remainder 1

47 / 2 = 23 remainder 1

23 / 2 = 11 remainder 1

11 / 2 = 5 remainder 1

5 / 2 = 2 remainder 1

2 / 2 = 1 remainder 0

1 / 2 = 0 remainder 1

  • 762 base 10 = 1011111010 base two

Then 0.78125 to binary:

0.78125 × 2 = 1 + 0.5625

0.5625 × 2 = 1 + 0.125

0.125 × 2 = 0 + 0.25

0.25 × 2 = 0 + 0.5

0.5 × 2 = 1 + 0

0.78125 base 10 = 0.11001 base two

Therefore, 762.78125 base 10 = 1011111010.11001 base two.

Learn more about base conversion at: brainly.com/question/17946394

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Answer:

A. P(X<20,000) = 0.0392

B. P(20,000 < x < 30,000) = 0.488

C. Amount = $39,070

Step-by-step explanation:

From XO group website

Cost of a wedding = $29,858

Mean, μ = $29,858

Standard Deviation, σ =$5,600

a. Calculating the probability that a wedding costs less than $20,000

P(X<20,000)?

First, the z value needs to be calculated.

z = (x - μ)/σ

x = 20,000

z = (20,000 - 29,858)/5600

z = -1.76

So, P(X<20,000) = P(Z<-1.76)

From the z table,

P(Z<-1.76) = 0.0392

P(X<20,000) = 0.0392

b. Calculating the probability that a wedding costs between $20,000 and $30,000

P(20,000 < x < 30,000)

First, the z value needs to be calculated.

z = (x - μ)/σ

When x = 20,000

z = (20,000 - 29,858)/5600

z = -1.76

When x = 30,000

z = (30,000 - 29,858)/5600

z = 0.02

P(20,000 < x < 30,000) = P(-1.76 < z <0.02) --- using the z table

P(-1.76 < z <0.02) = 0.508 - 0.0392

P(-1.76 < z <0.02) = 0.4688

P(20,000 < x < 30,000) = 0.488

c. Using the following formula, we'll get the amount it'll a wedding to be among the 5% most expensive

z = (x - μ)/σ where x = amount

Make x the subject of formula

x = σz + μ

Fist we need to get the z value of 5%

z0.05 = 1.645

x = σz + μ becomes

x = 5600 * 1.645 + 29,858

x = $39,070

Amount = $39,070

5 0
3 years ago
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